Czasopisma Naukowe w Sieci (CNS)

Asymptotic results for random polynomials on the unit circle

  1. Gabriel H. Tucci
  2. Philip Whiting

Abstract

In this paper we study the asymptotic behavior of the maximum magnitude of a complex random polynomial with i.i.d. uniformly distributed random roots on the unit circle. More specifically, let {nk}k=1 be an infinite sequence of positive integers and  let {zk}k=1 be a sequence of i.i.d. uniformly distributed random variables on the unit circle. The above pair of sequences determine a sequence of random polynomials PN(z)Nk=1 (z − zk)nk with random roots on the unit circle and their corresponding multiplicities. In this work, we show that subject to a certain regularity condition on the sequence {nk}k=1, the log maximum magnitude of these polynomials scales as sNI, where s2NNk=1 nk2 and I is a strictly positive random variable.

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Probability and Mathematical Statistics

34, z. 2, 2014

Strony od 181 do 197

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